Question: A circle has a circumference of $10\pi$. It has an arc of length $\dfrac{23}{3}\pi$. What is the central angle of the arc, in radians? ${10\pi}$ ${\dfrac{23}{15}\pi}$ $\color{#DF0030}{\dfrac{23}{3}\pi}$
The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{\theta}{2 \pi} = \dfrac{23}{3}\pi \div 10\pi$ $\dfrac{\theta}{2 \pi} = \dfrac{23}{30}$ $\theta = \dfrac{23}{30} \times 2 \pi$ $\theta = \dfrac{23}{15}\pi$ radians